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Geometry and Trigonometry / Lines, angles, and triangles Difficulty: Easy

In the figure, line $n$ intersects lines $r$ and $s$ . Line $r$ is parallel to line $s$ . What is the value of $x$ ?

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Explanation

The correct answer is $162$ . It's given that line $r$ is parallel to line $s$ . Since line $n$ intersects both lines $r$ and $s$ , it's a transversal. The angles in the figure marked as $162 degree$ and $x °$ are on the same side of the transversal, where one is an interior angle with line $s$ as a side, and the other is an exterior angle with line $r$ as a side. Thus, the marked angles are corresponding angles. When two parallel lines are intersected by a transversal, corresponding angles are congruent and, therefore, have equal measure. It follows that the value of $x$ is $162$ .